A064323 -id:A064323 - cp's OEIS frontend

A064324 a(n) = a(n-1) + floor(a(n-2)/2) with a(0)=1, a(1)=2.

1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 22, 30, 41, 56, 76, 104, 142, 194, 265, 362, 494, 675, 922, 1259, 1720, 2349, 3209, 4383, 5987, 8178, 11171, 15260, 20845, 28475, 38897, 53134, 72582, 99149, 135440, 185014, 252734, 345241, 471608, 644228, 880032

Offset: 0

Henry Bottomley, Sep 11 2001

nonn

a(n)/a(n-1) approaches (1+sqrt(3))/2 = 1.3660254... = A332133 for large n.

			a(5) = a(4)+floor(a(3)/2) = 4+floor(3/2) = 5.

Harry J. Smith, Table of n, a(n) for n = 0..400

Cf. A064323, A332133, A182229, A182230.

[n le 2 select n else Self(n-1)+Floor(Self(n-2)/2): n in [1..45]]; // Bruno Berselli, Apr 20 2012

RecurrenceTable[{a[n] == a[n-1] + Floor[a[n-2]/2], a[0] == 1, a[1] == 2}, a, {n, 0, 50}] (* G. C. Greubel, May 04 2019 *)
nxt[{a_,b_}]:={b,Floor[a/2]+b}; NestList[nxt,{1,2},50][[;;,1]] (* Harvey P. Dale, Jul 28 2023 *)

{ for (n=0, 400, if (n>1, a=a1 + a2\2; a2=a1; a1=a, if (n, a=a1=2, a=a2=1)); write("b064324.txt", n, " ", a) ) }; \\ Harry J. Smith, Sep 11 2009

a(n) = A064323(n) + 1.

A182230 a(n) = a(n-1)+floor(a(n-2)/4) with a(0)=3, a(1)=4.

Original entry on oeis.org

3, 4, 4, 5, 6, 7, 8, 9, 11, 13, 15, 18, 21, 25, 30, 36, 43, 52, 62, 75, 90, 108, 130, 157, 189, 228, 275, 332, 400, 483, 583, 703, 848, 1023, 1235, 1490, 1798, 2170, 2619, 3161, 3815, 4605, 5558, 6709, 8098, 9775, 11799, 14242, 17191, 20751, 25048, 30235

Offset: 0

Alex Ratushnyak, Apr 19 2012

nonn

a(n)/a(n-1) tends to (1+sqrt(2))/2 = 1.207106781186547524... [Bruno Berselli, Apr 23 2012]

Bruno Berselli, Table of n, a(n) for n = 0..1000

Cf. A064323, A064324, A182229, A182280; A174968.

a182230 n = a182230_list !! n
a182230_list = 3 : 4 : zipWith (+)
                       (map (flip div 4) a182230_list) (tail a182230_list)
-- Reinhard Zumkeller, Apr 30 2015

[n le 2 select n+2 else Self(n-1)+Floor(Self(n-2)/4): n in [1..52]]; // Bruno Berselli, Apr 20 2012

a:= proc(n) a(n):= a(n-1) +floor(a(n-2)/4) end: a(0), a(1):= 3, 4:
seq(a(n), n=0..60);  # Alois P. Heinz, Apr 20 2012

RecurrenceTable[{a[0] == 3, a[1] == 4, a[n] == a[n - 1] + Floor[a[n - 2]/4]}, a, {n, 51}] (* Bruno Berselli, Apr 21 2012 *)

prpr = 3
prev = 4
for i in range(2,55):
    current = prev + prpr//4
    print(current, end=',')
    prpr = prev
    prev = current

A173497 a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2), starting 2,1.

Original entry on oeis.org

2, 1, 2, 3, 4, 6, 8, 11, 15, 21, 29, 40, 55, 75, 103, 141, 193, 264, 361, 493, 674, 921, 1258, 1719, 2348, 3208, 4382, 5986, 8177, 11170, 15259, 20844, 28474, 38896, 53133, 72581, 99148, 135439, 185013, 252733, 345240, 471607, 644227, 880031

Offset: 0

Roger L. Bagula, Nov 23 2010

nonn

The limiting ratio is a(n+1)/a(n): 1.36602540378443.

This limiting ratio is (1+sqrt(3))/2. - Robert Israel, Aug 30 2020

Robert Israel, Table of n, a(n) for n = 0..7374

Cf. A064323, A000032.

A[0]:= 2: A[1]:= 1:
for n from 2 to 100 do
  A[n]:= A[n-1]+A[n-2]-floor(A[n-2]/2)
od:
seq(A[i],i=0..100); # Robert Israel, Aug 30 2020

l[0] = 2; l[1] = 1;
l[n_] := l[n] = l[n - 1] + l[n - 2] - Floor[l[n - 2]/2]
Table[l[n], {n, 0, 30}]
RecurrenceTable[{a[0]==2,a[1]==1,a[n]==a[n-1]+a[n-2]-Floor[a[n-2]/2]},a,{n,50}] (* Harvey P. Dale, Apr 26 2016 *)

a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2).

More terms from Max Alekseyev, Jun 18 2011

A173508 a(n) = ceiling(A173497(n)/2).

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 6, 8, 11, 15, 20, 28, 38, 52, 71, 97, 132, 181, 247, 337, 461, 629, 860, 1174, 1604, 2191, 2993, 4089, 5585, 7630, 10422, 14237, 19448, 26567, 36291, 49574, 67720, 92507, 126367, 172620, 235804, 322114

Offset: 0

Roger L. Bagula, Nov 23 2010

nonn

Cf. A000032, A064323, A173497.

A173497 := proc(n) option remember; if n <= 1 then op(n+1,[2,1]) ; else             procname(n-1)+procname(n-2)-floor(procname(n-2)/2) ; end if; end proc:
A173508 := proc(n) ceil(A173497(n)/2) ; end proc:
seq(A173508(n),n=0..60) ;

Definition corrected, Mma code related to another sequence removed, sequence extended

cp's OEIS Frontend

A064324 a(n) = a(n-1) + floor(a(n-2)/2) with a(0)=1, a(1)=2.

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A182230 a(n) = a(n-1)+floor(a(n-2)/4) with a(0)=3, a(1)=4.

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A173497 a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2), starting 2,1.

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A173508 a(n) = ceiling(A173497(n)/2).

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